Let Ba,b be a weighted-fractional Brownian motion with Hurst indexes a and b such that a > −1 and 0 ≼ b ≺ 1∧ (1 + a). In this paper, we consider the linear self-attracting diffusion \(dX_{t}^{a,b}=dB_{t}^{a,b}-\theta \left(\int_{0}^{t}(X_{t}^{a,b}-X_{s}^{a,b})ds\right)dt+\nu dt\) with X 0 a,b = 0, where θ > 0 and \(\nu \in \mathbb{R}\) are two real parameters. The model is an analog of the linear self-interacting diffusion (see Cranston and Le Jan (1995)). Under the continuous observation, we study asymptotic behaviors of the least squares estimators \(\hat{\theta}_{T}\) and \(\hat{\nu}_{T}\) . In particular, when \(b >{1 \over 2}\) we obtain a new random variable Z 1 a,b which is called the Rosenblatt random variable if a = 0, and we show that \(C_{a,b}T^{2-2b}(\hat{\theta}_{T}-\theta)\) converges in distribution to the sum of the chi-square random variable with i degree of freedom and the random variable Z 1 a,b .
